There is also the introduction of a “modified function” by which we can use Lagrange's equations for some of the coordinates and Hamilton's equations for the others.

Furthermore, the most general quasilinear equation of the above form is found that can be mapped via a hodograph transformation to a semilinear form. This algorithm provides a method for establishing ...

This procedure is based upon the reducibility of LODE of the second order to the equation with constant coefficients by Kummer-Liouville transformation [3]. It is applicable not only to the equations ...